Find the potential energy of a system of four particles placed at the vertices of a square of side 1. Also obtain the potential at the centre of the square.

Explanation

Consider four masses each of mass m at the corners of a square of side 1. see fig. we have four mass pairs at distance 1 and two diagonal pairs at distance `sqrt(2)l`
Hence, `U(r) = -(4)(Gm^(2))/(1) - 2(Gm^(2))/(sqrt(2)l)`
`= -(2Gm^(2))/(1)(2+(1)/(sqrt(2))) = -5.41(Gm^(2))/(1)`
The gravitational potential at the centre of the square `(r = sqrt(2)l//2)` is `V(r) = -4sqrt(2)(Gm)/(1)`